The official cinematic reveal of Mass Effect: Andromeda is here, and it definitely is just that: cinematic.
It seemed odd to not see Commander Shepard, but as I watched, things definitely worked for me, and I think that they will probably work for you too.
Furthermore, the Mass Effect: Andromeda Initiative recruitment page was launched, and it can provide you with some further back story to the game.
The date at the top right of the page is 2184, the year before the events of Mass Effect 2. If you go further into the website, you can find the briefing page, which outlines the plans for deep space exploration:
Essentially, if you join the mission, you will awake in 600 years on the outskirts of the Andromeda galaxy. Three Ark ships will be leaving the Milky Way galaxy at the same time, each ship carrying a different species.
The goal is to explore, but, of course, things are not going to go as planned.
Mass Effect: Andromeda releases Spring of 2017.